Yes, the EU does have a right to voice opposition to Luxembourg's helping Amazon avoid taxes.

Taxes are meant for all. They are a necessary evil. When Luxembourg helped Amazon avoid the VAT taxes, they were essentially spitting in the EU's face. Since Luxembourg is a part of the European Economy, the laws effecting other European countries should be followed by them. Amazon should have to pay EU taxes in this small country also.

The EU should examine how Luxembourg helps Amazon avoid taxes

If Luxembourg is helping Amazon avoid paying taxes, the EU should analyze this and determine if it is legal, or perhaps close up some loopholes in the system so that Amazon will have to start paying taxes. Amazon is a corporation worth billions of dollars and they should be responsible for paying taxes like any other company. Taxes help local governments function and because Amazon is responsible for such a large share of consumer goods, the amount of lost tax revenue is significant.

Yes, the EU has a right to complain about Luxembourg's actions.

Yes, the EU has a right to complain about Luxembourg's actions regarding the tax evasion of Amazon. Amazon is a world-wide company that does not have any special rights that excludes it from paying taxes, and the fact that Luxembourg has helped the company evade paying these taxes is deplorable.

No countries have a right to attract business

Many nations out there are not blessed with an abundance of natural resources to rely on in contributing to a strong economy so they need to create other incentives to attract business to their countries. This is a common tactic for small nations to attract business/investment and should not be discouraged.